Integrated learning of linear representations

While the importance of representations for recognition has been widely recognized, in practice the choice of representations is often limited and applications are forced to choose relatively the best one among the available. In this paper, we advocate an integrated learning framework where the representation is learned with respect to a chosen performance criterion. For linear representations, this problem is posed as an optimization one on the underlying manifold determined by the constraints of the application, where the manifolds related to typical applications are given. To develop computationally effective algorithms, the underlying geometric structures are exploited. We demonstrate the feasibility and effectiveness of the proposed framework by finding optimal linear filters for recognition with other additional properties.